A general proof of the conservation of the curvature perturbation

Abstract

Without invoking a perturbative expansion, we define the cosmological curvature perturbation, and consider its behaviour assuming that the universe is smooth over a sufficiently large comoving scale. The equations are simple, resembling closely the first-order equations, and they lead to results which generalise those already proven in linear perturbation theory and (in part) in second-order perturbation theory. In particular, the curvature perturbation is conserved provided that the pressure is a unique function of the energy density.

Comments: 9 pages, revtex4, no figures; v2: 14 pages, main body and appendix extended, typos corrected, references added; v3: minor changes, typos corrected, references added